Gogoberidze was married, since 1958, to the architect Vladimir Aleksi-Meskhishvili (died 1978), with two daughters.
Vladimir Aleksi-Meskhishvili was born in Tbilisi, graduated from the Industrial Institute of Georgia in 1939 and taught at Tbilisi Polytechnic University since 1955.
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He had four children, including the now-United States-based set designer Gogi Aleksi-Meskhishvili.
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